Giovanni Gallavotti
Ergodic and chaotic hypotheses: nonequilibrium
ensembles in statistical mechanics and turbulence
(77K, latex-revtex)
ABSTRACT. The ergodic hypothesis outgrew from the
ancient conception of motion as periodic or quasi periodic. It did
cause a revision of our views of motion, particularly through
Boltzmann and Poincar\'e: we discuss how Boltmann's conception of
motion is still very modern and how it can provide ideas and methods
to study the problem of nonequilibrium in mechanics and in
fluids. This leads to the chaotic hypothesis, a recent interpretation
of a very ambitious principle conceived by D. Ruelle: it is a possible
extension of the ergodic hypothesis and it implies general
parameterless relations. Together with further ideas, it appears to be
consistent with some recent experiments as we discuss here.